Calculate angle ratios, split a total angle by ratio, or find the missing angle from two related angles in degrees or radians for angle comparison.
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Angle Ratio Formula
The calculator uses one of three formulas depending on the mode you select.
Find ratio (compare two angles):
Ratio = A / B
Split total (divide a total angle by a ratio):
Angle A = Total * a / (a + b) Angle B = Total * b / (a + b)
Find angle (one angle and the ratio are known):
Other angle = Known * (other term / known term)
- A, B — the two angles being compared
- a, b — the ratio terms (a:b)
- Total — the combined angle being split
Both angles must use the same unit before applying the formula. The calculator converts radians to degrees internally, so you can mix units in the inputs. Ratio terms must be positive. Negative or zero angles are not accepted.
Common Angle Totals and Ratios
Use these as reference points when setting up a split or checking a result.
| Total angle | Where it appears | Radians |
|---|---|---|
| 90° | Complementary angles, right angle | π/2 |
| 180° | Straight angle, triangle angle sum | π |
| 270° | Three-quarter turn | 3π/2 |
| 360° | Full circle, angles around a point | 2π |
| 540° | Pentagon interior angle sum | 3π |
| Ratio A:B | Split of 90° | Split of 180° | Split of 360° |
|---|---|---|---|
| 1:1 | 45°, 45° | 90°, 90° | 180°, 180° |
| 1:2 | 30°, 60° | 60°, 120° | 120°, 240° |
| 1:3 | 22.5°, 67.5° | 45°, 135° | 90°, 270° |
| 2:3 | 36°, 54° | 72°, 108° | 144°, 216° |
| 3:5 | 33.75°, 56.25° | 67.5°, 112.5° | 135°, 225° |
Worked Example
Two complementary angles are in the ratio 2:7. Find each angle.
- Sum of ratio terms: 2 + 7 = 9
- Angle A = 90° × (2 / 9) = 20°
- Angle B = 90° × (7 / 9) = 70°
- Check: 20° + 70° = 90°. Ratio 20:70 simplifies to 2:7.
FAQ
Does the order of the ratio matter? Yes. 2:3 and 3:2 produce different angles. The first term always corresponds to Angle A.
Can I use radians? Yes. Switch the unit dropdown next to any angle field. The ratio itself is unitless, so 1:2 means the same thing in degrees and radians.
Why does the ratio show "≈"? The calculator approximates the simplest integer ratio within a denominator limit of 500. If the exact ratio is irrational or has very large terms, the displayed ratio is a close approximation.
What if the two angles are equal? The ratio is 1:1 and each angle is half the total.